Magnetorotational instability in protoplanetary discs: The effect of dust grains

We investigate the linear growth and vertical structure of the MRI in protoplanetary discs when dust grains are well mixed with the gas over the entire disc thickness. All the grains have the same radius (a = 0.1, 1 or 3 micron) and constitute 1 % of the total mass of the gas. Solutions are obtained at R = 5 and 10 AU for a minimum-mass solar nebula model and different choices of the initially vertical magnetic field strength (B), configuration of the diffusivity tensor and grain sizes. We find that when no grains are present, or they are > 1 micron, the midplane remains magnetically coupled for B up to a few gauss at both radii. In contrast, when a population of small grains (a = 0.1 micron) is present, the disc is magnetically inactive for z/H < 2 and only B < 50 mG couple to the fluid. At 5 AU, Ohmic diffusion dominates for z/H < 1 when B < a few mG, irrespective of the properties of the grain population. Conversely, at 10 AU this diffusion term is unimportant in all the scenarios studied here. For z/H > 5, ambipolar diffusion is severe and prevents the field from coupling to the gas for all B. Hall diffusion is dominant for a wide range of field strengths at both radii when dust grains are present. The growth rate, wavenumber and range of magnetic field strengths for which MRI-unstable modes exist are all drastically diminished when dust grains are present, particularly when they are small (a ~ 0.1 micron). We conclude that in protoplanetary discs, the magnetic field is able to couple to the gas and shear over a wide range of fluid conditions even when small dust grains are well mixed with the gas. Despite the low magnetic coupling, MRI modes grow for an extended range of magnetic field strengths and Hall diffusion largely determines the properties of the perturbations in the inner regions of the disc (abridged).Comment: 17 pages, 11 figures. Submitted to MNRA

Understanding Spatial and Spectral Morphologies of Ultracompact H II Regions

The spatial morphology, spectral characteristics, and time variability of ultracompact H II regions provide strong constraints on the process of massive star formation. We have performed simulations of the gravitational collapse of rotating molecular cloud cores, including treatments of the propagation of ionizing and non-ionizing radiation. We here present synthetic radio continuum observations of H II regions from our collapse simulations, to investigate how well they agree with observation, and what we can learn about how massive star formation proceeds. We find that intermittent shielding by dense filaments in the gravitationally unstable accretion flow around the massive star leads to highly variable H II regions that do not grow monotonically, but rather flicker, growing and shrinking repeatedly. This behavior appears able to resolve the well-known lifetime problem. We find that multiple ionizing sources generally form, resulting in groups of ultracompact H II regions, consistent with observations. We confirm that our model reproduces the qualitative H II region morphologies found in surveys, with generally consistent relative frequencies. We also find that simulated spectral energy distributions (SEDs) from our model are consistent with the range of observed H II region SEDs, including both regions showing a normal transition from optically thick to optically thin emission, and those with intermediate spectral slopes. In our models, anomalous slopes are solely produced by inhomogeneities in the H II region, with no contribution from dust emission at millimeter or submillimeter wavelengths. We conclude that many observed characteristics of ultracompact H II regions appear consistent with massive star formation in fast, gravitationally unstable, accretion flows.Comment: ApJ in pres

Rapid planetesimal formation in turbulent circumstellar discs

The initial stages of planet formation in circumstellar gas discs proceed via dust grains that collide and build up larger and larger bodies (Safronov 1969). How this process continues from metre-sized boulders to kilometre-scale planetesimals is a major unsolved problem (Dominik et al. 2007): boulders stick together poorly (Benz 2000), and spiral into the protostar in a few hundred orbits due to a head wind from the slower rotating gas (Weidenschilling 1977). Gravitational collapse of the solid component has been suggested to overcome this barrier (Safronov 1969, Goldreich & Ward 1973, Youdin & Shu 2002). Even low levels of turbulence, however, inhibit sedimentation of solids to a sufficiently dense midplane layer (Weidenschilling & Cuzzi 1993, Dominik et al. 2007), but turbulence must be present to explain observed gas accretion in protostellar discs (Hartmann 1998). Here we report the discovery of efficient gravitational collapse of boulders in locally overdense regions in the midplane. The boulders concentrate initially in transient high pressures in the turbulent gas (Johansen, Klahr, & Henning 2006), and these concentrations are augmented a further order of magnitude by a streaming instability (Youdin & Goodman 2005, Johansen, Henning, & Klahr 2006, Johansen & Youdin 2007) driven by the relative flow of gas and solids. We find that gravitationally bound clusters form with masses comparable to dwarf planets and containing a distribution of boulder sizes. Gravitational collapse happens much faster than radial drift, offering a possible path to planetesimal formation in accreting circumstellar discs.Comment: To appear in Nature (30 August 2007 issue). 18 pages (in referee mode), 3 figures. Supplementary Information can be found at 0708.389

Wind-driving protostellar accretion discs. I. Formulation and parameter constraints

We study a model of weakly ionized, protostellar accretion discs that are threaded by a large-scale, ordered magnetic field and power a centrifugally driven wind. We consider the limiting case where the wind is the main repository of the excess disc angular momentum and generalize the radially localized disc model of Wardle & K\"onigl (1993), which focussed on the ambipolar diffusion regime, to other field diffusivity regimes, notably Hall and Ohm. We present a general formulation of the problem for nearly Keplerian, vertically isothermal discs using both the conductivity-tensor and the multi-fluid approaches and simplify it to a normalized system of ordinary differential equations in the vertical space coordinate. We determine the relevant parameters of the problem and investigate, using the vertical-hydrostatic-equilibrium approximation and other simplifications, the parameter constraints on physically viable solutions for discs in which the neutral particles are dynamically well coupled to the field already at the midplane. When the charged particles constitute a two-component ion--electron plasma one can identify four distinct sub-regimes in the parameter domain where the Hall diffusivity dominates and three sub-regimes in the Ohm-dominated domain. Two of the Hall sub-regimes can be characterized as being ambipolar diffusion-like and two as being Ohm-like. When the two-component plasma consists instead of positively and negatively charged grains of equal mass, the entire Hall domain and one of the Ohm sub-regimes disappear. In all viable solutions the midplane neutral--ion momentum exchange time is shorter than the local orbital time. Vertical magnetic squeezing always dominates over gravitational tidal compression in this model. (Abridged)Comment: 23 pages, 2 figures, 4 tables; accepted for publication in MNRA

Magnetic fields in protoplanetary disks

Magnetic fields likely play a key role in the dynamics and evolution of protoplanetary discs. They have the potential to efficiently transport angular momentum by MHD turbulence or via the magnetocentrifugal acceleration of outflows from the disk surface, and magnetically-driven mixing has implications for disk chemistry and evolution of the grain population. However, the weak ionisation of protoplanetary discs means that magnetic fields may not be able to effectively couple to the matter. I present calculations of the ionisation equilibrium and magnetic diffusivity as a function of height from the disk midplane at radii of 1 and 5 AU. Dust grains tend to suppress magnetic coupling by soaking up electrons and ions from the gas phase and reducing the conductivity of the gas by many orders of magnitude. However, once grains have grown to a few microns in size their effect starts to wane and magnetic fields can begin to couple to the gas even at the disk midplane. Because ions are generally decoupled from the magnetic field by neutral collisions while electrons are not, the Hall effect tends to dominate the diffusion of the magnetic field when it is able to partially couple to the gas. For a standard population of 0.1 micron grains the active surface layers have a combined column of about 2 g/cm^2 at 1 AU; by the time grains have aggregated to 3 microns the active surface density is 80 g/cm^2. In the absence of grains, x-rays maintain magnetic coupling to 10% of the disk material at 1 AU (150 g/cm^2). At 5 AU the entire disk thickness becomes active once grains have aggregated to 1 micron in size.Comment: 11 pages, 11 figs, aastex.cls. Accepted for publication in Astrophysics & Space Science. v3 corrects bibliograph

Evidence for the formation of comet 67P/Churyumov-Gerasimenko through gravitational collapse of a bound clump of pebbles

The processes that led to the formation of the planetary bodies in the Solar System are still not fully understood. Using the results obtained with the comprehensive suite of instruments on-board ESA’s Rosetta mission, we present evidence that comet 67P/Churyumov-Gerasimenko likely formed through the gentle gravitational collapse of a bound clump of mm-sized dust aggregates (“pebbles”), intermixed with microscopic ice particles. This formation scenario leads to a cometary make-up that is simultaneously compatible with the global porosity, homogeneity, tensile strength, thermal inertia, vertical temperature profiles, sizes and porosities of emitted dust, and the steep increase in water-vapour production rate with decreasing heliocentric distance, measured by the instruments on-board the Rosetta spacecraft and the Philae lander. Our findings suggest that the pebbles observed to be abundant in protoplanetary discs around young stars provide the building material for comets and other minor bodies

Magnetorotational instability in protoplanetary discs

We investigate the linear growth and vertical structure of the magnetorotational instability (MRI) in weakly ionised, stratified accretion discs. The magnetic field is initially vertical and dust grains are assumed to have settled towards the midplane, so charges are carried by electrons and ions only. Solutions are obtained at representative radial locations from the central protostar for different choices of the initial magnetic field strength, sources of ionisation, and disc surface density. The MRI is active over a wide range of magnetic field strengths and fluid conditions in low conductivity discs. For the minimum-mass solar nebula model, incorporating cosmic ray ionisation, perturbations grow at 1 AU for B < 8 G. For a significant subset of these strengths (0.2 - 5 G), the growth rate is of order the ideal MHD rate (0.75 Omega). Similarly, when cosmic rays are assumed to be excluded from the disc by the winds emitted by the magnetically active protostar, unstable modes grow at this radius for B less than about 2 G. This study shows that, despite the low magnetic coupling, the magnetic field is dynamically important for a large range of fluid conditions and field strengths in protostellar discs. Hall diffusion largely determines the structure and growth rate of these perturbations for all studied radii. At radii of order 1 AU, in particular, it is crucial to incorporate the full conductivity tensor in studies of the dynamics of astrophysical discs. (Abridged)Comment: 26 pages, 15 figures, submitted to MNRA

Matlab fig files for the paper 'Experimental gas-fluidized bed drying study on the segregation and mixing dynamics for binary and ternary solids'

This is a set of Matlab .fig files corresponding to the figures in the paper 'Experimental gas-fluidized bed drying study on the segregation and mixing dynamics for binary and ternary solids' published in Chemical Engineering Journal. In this study, experiments in a pseudo-2D fluidized bed setup were performed to obtain insight in the complex and changing bed hydrodynamics and its interplay with mass and heat transfer. The data was obtained by using a combined Particle Image Velocimetry (PIV), Digital Image Analysis (DIA) and Infrared (IR) technique. Furthermore, a machine learning algorithm was applied in order to determine the segregation and mixing dynamics. The dataset consists of the following .fig files whereof a short description is given below: Figure 3: Minimum fluidization velocity determination using the mean pressure drop over the bed. Figure 4: Precision-recall analysis Figure 8: Segregation index based on the average height of the medium and large-sized solids.Figure 9: Segregation index based on the average height of the medium and large-sized solids.Figure 10 A, B, C and D: Time-averaged solids volume fluxes for the u0=0.975 m/s drying case at four different times.Figure 11 A, B, C and D: Time-averaged solids volume fluxes for the u0=1.17 m/s drying case at four different times.Figure 12 A, B, C and D: Time-averaged solids volume fluxes for the u0=1.365 m/s drying case at four different times.Figure 13 A and B: Mean particle temperature and standard deviation over time for the three different superficial gas velocities. Figure 17 A and B: Segregation indices based on the average height of the small, medium and large-sized solids.Figure 18 A, B, C and D: Time-averaged solids volume fluxes for the u0=0.7875 m/s drying case at four different times.Figure 19 A, B, C and D: Time-averaged solids volume fluxes for the u0=0.945 m/s drying case at four different times.Figure 20 A, B, C and D: Time-averaged solids volume fluxes for the u0=1.1025 m/s drying case at four different times.Figure 21 A and B: Mean particle temperature and standard deviation over time for the three different superficial gas velocities